Why has spacetime torsion such negligible effect on the Universe?

Abstract

We attempt an answer to the question as to why the evolution of a four-dimensional universe is governed by spacetime curvature but not torsion. An answer is found if there is an additional compact spacelike dimension with a warped geometry, with torsion caused by a Kalb-Ramond (KR) antisymmetric tensor field in the bulk. Starting from a Randall-Sundrum type of warped extra dimension, and including the inevitable backreaction ensuing from the radius stabilization mechanism, we show that there is always an extra exponential suppression of the KR field on the four-dimensional projection that constitutes our visible Universe. The backreaction is found to facilitate the process of such suppression.